# Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality

### Submission summary

 Authors (as Contributors): Weicheng Ye · Liujun Zou
Submission information
Date accepted: 2022-08-08
Date submitted: 2022-07-05 21:06
Submitted by: Zou, Liujun
Submitted to: SciPost Physics
Ontological classification
Specialties:
• Condensed Matter Physics - Theory
• High-Energy Physics - Theory
• Mathematical Physics
• Statistical and Soft Matter Physics
Approach: Theoretical

### Abstract

Lieb-Schultz-Mattis (LSM) theorems provide powerful constraints on the emergibility problem, i.e. whether a quantum phase or phase transition can emerge in a many-body system. We derive the topological partition functions that characterize the LSM constraints in spin systems with $G_s\times G_{int}$ symmetry, where $G_s$ is an arbitrary space group in one or two spatial dimensions, and $G_{int}$ is any internal symmetry whose projective representations are classified by $\mathbb{Z}_2^k$ with $k$ an integer. We then apply these results to study the emergibility of a class of exotic quantum critical states, including the well-known deconfined quantum critical point (DQCP), $U(1)$ Dirac spin liquid (DSL), and the recently proposed non-Lagrangian Stiefel liquid. These states can emerge as a consequence of the competition between a magnetic state and a non-magnetic state. We identify all possible realizations of these states on systems with $SO(3)\times \mathbb{Z}_2^T$ internal symmetry and either $p6m$ or $p4m$ lattice symmetry. Many interesting examples are discovered, including a DQCP adjacent to a ferromagnet, stable DSLs on square and honeycomb lattices, and a class of quantum critical spin-quadrupolar liquids of which the most relevant spinful fluctuations carry spin-$2$. In particular, there is a realization of spin-quadrupolar DSL that is beyond the usual parton construction. We further use our formalism to analyze the stability of these states under symmetry-breaking perturbations, such as spin-orbit coupling. As a concrete example, we find that a DSL can be stable in a recently proposed candidate material, NaYbO$_2$.

Published as SciPost Phys. 13, 066 (2022)

We thank the editor for dealing with our draft, and all referees for their constructive comments and suggestions. The response to each report is given under the report, and a summary of changes is attached below.

### List of changes

Besides various minor changes, the major changes in the revised draft are summarized as follows.

1. In Sec. III A, we add a sentence to explicitly point out that the symmetries, anomalies and dynamical properties of the Stiefel liquids reviewed there serve as an intrinsic definition of Stiefel liquids, without explicitly referring to any Lagrangian.

2. In the introduction, we add a footnote to clarify the relation between the current paper and arXiv: 2101.07805, and in the present paper we correct some mistakes in arXiv: 2101.07805.

3. We have split the paragraph in the right column of page 8 into two paragraphs.

4. We have changed the last paragraph of the introduction to briefly summarize the main results.

### Submission & Refereeing History

Resubmission scipost_202202_00032v2 on 5 July 2022
Submission scipost_202202_00032v1 on 16 February 2022

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